I have moved our B315s wireless broadband modem to a RBI setup at another location outside of Auckland and it worked just fine. They are not locked to a tower. It's the SIM is locked to the B315s so you can't take the SIM and plug it into another device. I am pretty sure you could move the modem around and it would just connect to your providers cell towers, at this stage anyway.
We are within 1.5Km of the nearest cabinet and were getting sub 10Mbps DSL. Internal home wiring checked out by multiple technicians. Street to house to be a different story. No point in people going out and spending $300-$400 bucks on the latest DSL router that will fix your DSL woes.
I do suspect there must be some form of 'control' on the download speeds you get from towers. If not initially on residential wireless broadband then definitely now.
https://gis.geek.nz/celltowers